The hybrid power mean of the quartic Gauss sums and the two-term exponential sums
In this paper, we use the analytic method and the properties of classical Gauss sums to study the computational problems of one kind hybrid power mean of quartic Gauss sums and two-term exponential sums, and give an interesting fourth-order linear recurrence formula for it.
Saved in:
| Published in | Advances in difference equations Vol. 2018; no. 1; pp. 1 - 10 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Cham
Springer International Publishing
11.07.2018
Springer Nature B.V SpringerOpen |
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | In this paper, we use the analytic method and the properties of classical Gauss sums to study the computational problems of one kind hybrid power mean of quartic Gauss sums and two-term exponential sums, and give an interesting fourth-order linear recurrence formula for it. |
|---|---|
| AbstractList | Abstract In this paper, we use the analytic method and the properties of classical Gauss sums to study the computational problems of one kind hybrid power mean of quartic Gauss sums and two-term exponential sums, and give an interesting fourth-order linear recurrence formula for it. In this paper, we use the analytic method and the properties of classical Gauss sums to study the computational problems of one kind hybrid power mean of quartic Gauss sums and two-term exponential sums, and give an interesting fourth-order linear recurrence formula for it. |
| ArticleNumber | 236 |
| Author | Li, Xiaoxue |
| Author_xml | – sequence: 1 givenname: Xiaoxue surname: Li fullname: Li, Xiaoxue email: lxx20072012@163.com organization: Faculty of Science, Xi’an Aeronautical University |
| BookMark | eNp9kUtLxDAUhYMoqKM_wF3AdTWP5rUU8QWCCLoOaZKOHWaaMUnx8evNtIoi6Ope7j3f4cDZB9t96D0ARxidYCz5acKUc1IhLCvMmazet8Ae5lJUWNZi-8e-C_ZTWiBEVC3lHrh_ePLw6a2JnYPr8OIjXHnTw9DCXB7Pg4m5s_DKDCnBNKwSNL0bX_klVNnHFfSv6xKlz51ZjooDsNOaZfKHn3MGHi8vHs6vq9u7q5vzs9vK1oTlytRWeaMwUZwpa2qBnbCMI1GODWPOI0wFbVgrlJVEOC4VNS1jiDcNd87QGbiZfF0wC72O3crENx1Mp8dDiHM9hl96jahXDa3rtvjX0hFFuRBMEtoqa_nodTx5rWN4HnzKehGG2Jf4miAuKVYci6ISk8rGkFL0rbZdNrkLfY6mW2qM9KYLPXWhSxd604V-LyT-RX7l_Y8hE5OKtp_7-J3pb-gDR5adqg |
| CitedBy_id | crossref_primary_10_3934_math_2024183 crossref_primary_10_3934_era_2025071 |
| Cites_doi | 10.1016/j.jnt.2005.04.001 10.4064/aa101-2-5 10.1016/j.jnt.2013.10.022 10.1007/s10587-014-0082-0 10.1186/s13662-017-1097-2 10.1515/math-2017-0104 10.1515/math-2017-0014 |
| ContentType | Journal Article |
| Copyright | The Author(s) 2018 Advances in Difference Equations is a copyright of Springer, (2018). All Rights Reserved. |
| Copyright_xml | – notice: The Author(s) 2018 – notice: Advances in Difference Equations is a copyright of Springer, (2018). All Rights Reserved. |
| DBID | C6C AAYXX CITATION 3V. 7SC 7TB 7XB 8AL 8FD 8FE 8FG 8FK ABJCF ABUWG AFKRA ARAPS AZQEC BENPR BGLVJ CCPQU DWQXO FR3 GNUQQ HCIFZ JQ2 K7- KR7 L6V L7M L~C L~D M0N M7S P5Z P62 PHGZM PHGZT PIMPY PKEHL PQEST PQGLB PQQKQ PQUKI PRINS PTHSS Q9U DOA |
| DOI | 10.1186/s13662-018-1658-z |
| DatabaseName | Springer Nature OA Free Journals CrossRef ProQuest Central (Corporate) Computer and Information Systems Abstracts Mechanical & Transportation Engineering Abstracts ProQuest Central (purchase pre-March 2016) Computing Database (Alumni Edition) Technology Research Database ProQuest SciTech Collection ProQuest Technology Collection ProQuest Central (Alumni) (purchase pre-March 2016) Materials Science & Engineering Collection ProQuest Central (Alumni) ProQuest Central UK/Ireland Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Central Technology Collection ProQuest One Community College ProQuest Central Engineering Research Database ProQuest Central Student SciTech Premium Collection ProQuest Computer Science Collection Computer Science Database Civil Engineering Abstracts ProQuest Engineering Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional Computing Database ProQuest Engineering Database ProQuest Advanced Technologies & Aerospace Database ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Premium ProQuest One Academic Publicly Available Content Database ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic ProQuest One Academic UKI Edition ProQuest Central China Engineering collection ProQuest Central Basic Directory of Open Access Journals (DOAJ) |
| DatabaseTitle | CrossRef Publicly Available Content Database Computer Science Database ProQuest Central Student Technology Collection Technology Research Database Computer and Information Systems Abstracts – Academic ProQuest One Academic Middle East (New) Mechanical & Transportation Engineering Abstracts ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Computer Science Collection Computer and Information Systems Abstracts ProQuest Central (Alumni Edition) SciTech Premium Collection ProQuest One Community College ProQuest Central China ProQuest Central ProQuest One Applied & Life Sciences ProQuest Engineering Collection ProQuest Central Korea ProQuest Central (New) Advanced Technologies Database with Aerospace Engineering Collection Advanced Technologies & Aerospace Collection Civil Engineering Abstracts ProQuest Computing Engineering Database ProQuest Central Basic ProQuest Computing (Alumni Edition) ProQuest One Academic Eastern Edition ProQuest Technology Collection ProQuest SciTech Collection Computer and Information Systems Abstracts Professional Advanced Technologies & Aerospace Database ProQuest One Academic UKI Edition Materials Science & Engineering Collection Engineering Research Database ProQuest One Academic ProQuest One Academic (New) ProQuest Central (Alumni) |
| DatabaseTitleList | Publicly Available Content Database |
| Database_xml | – sequence: 1 dbid: C6C name: Springer Nature OA Free Journals url: http://www.springeropen.com/ sourceTypes: Publisher – sequence: 2 dbid: DOA name: DOAJ Directory of Open Access Journals url: https://www.doaj.org/ sourceTypes: Open Website – sequence: 3 dbid: 8FG name: ProQuest Technology Collection url: https://search.proquest.com/technologycollection1 sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Mathematics |
| EISSN | 1687-1847 |
| EndPage | 10 |
| ExternalDocumentID | oai_doaj_org_article_03e9b344f56048d2936775823f9cc6da 10_1186_s13662_018_1658_z |
| GrantInformation_xml | – fundername: National Natural Science Foundation of China grantid: 11771351; 11501452 funderid: http://dx.doi.org/10.13039/501100001809 – fundername: Scientific Research Project of Xi'an Aeronatical University grantid: 2018KY0208 |
| GroupedDBID | -A0 23M 2WC 3V. 4.4 40G 5GY 5VS 6J9 8FE 8FG 8R4 8R5 AAFWJ AAYZJ ABDBF ABJCF ABUWG ACGFO ACGFS ACIPV ACIWK ACUHS ADBBV ADINQ AEGXH AENEX AFKRA AFPKN AHBYD AHYZX AIAGR ALMA_UNASSIGNED_HOLDINGS AMKLP AMTXH ARAPS AZQEC BAPOH BCNDV BENPR BGLVJ BPHCQ C24 C6C CCPQU CS3 DWQXO EBS EJD ESX GNUQQ GROUPED_DOAJ H13 HCIFZ J9A K6V K7- KQ8 L6V M0N M7S M~E OK1 P2P P62 PIMPY PQQKQ PROAC PTHSS Q2X REM RHU RNS RSV SMT SOJ TUS U2A UPT ~8M AAYXX CITATION OVT PHGZM PHGZT 7SC 7TB 7XB 8AL 8FD 8FK FR3 JQ2 KR7 L7M L~C L~D PKEHL PQEST PQGLB PQUKI PRINS Q9U PUEGO |
| ID | FETCH-LOGICAL-c425t-a4c9ea9129659ca471d7c5607ea9b55de01373b5f79c827d6893af5506bb6dda3 |
| IEDL.DBID | DOA |
| ISSN | 1687-1847 1687-1839 |
| IngestDate | Wed Aug 27 00:10:47 EDT 2025 Fri Jul 25 12:19:34 EDT 2025 Tue Jul 01 03:30:04 EDT 2025 Thu Apr 24 23:02:18 EDT 2025 Fri Feb 21 02:36:02 EST 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 1 |
| Keywords | Quartic Gauss sums Analytic method 11L05 11L07 Two-term exponential sums Hybrid power mean |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c425t-a4c9ea9129659ca471d7c5607ea9b55de01373b5f79c827d6893af5506bb6dda3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| OpenAccessLink | https://doaj.org/article/03e9b344f56048d2936775823f9cc6da |
| PQID | 2068319617 |
| PQPubID | 237355 |
| PageCount | 10 |
| ParticipantIDs | doaj_primary_oai_doaj_org_article_03e9b344f56048d2936775823f9cc6da proquest_journals_2068319617 crossref_citationtrail_10_1186_s13662_018_1658_z crossref_primary_10_1186_s13662_018_1658_z springer_journals_10_1186_s13662_018_1658_z |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2018-07-11 |
| PublicationDateYYYYMMDD | 2018-07-11 |
| PublicationDate_xml | – month: 07 year: 2018 text: 2018-07-11 day: 11 |
| PublicationDecade | 2010 |
| PublicationPlace | Cham |
| PublicationPlace_xml | – name: Cham – name: New York |
| PublicationTitle | Advances in difference equations |
| PublicationTitleAbbrev | Adv Differ Equ |
| PublicationYear | 2018 |
| Publisher | Springer International Publishing Springer Nature B.V SpringerOpen |
| Publisher_xml | – name: Springer International Publishing – name: Springer Nature B.V – name: SpringerOpen |
| References | Cochrane, Pinner (CR8) 2006; 116 Li, Hu (CR2) 2017; 15 Zhang, Hu (CR11) 2018; 20 Apostol (CR13) 1976 Shen, Zhang (CR1) 2017; 2017 Zhang, Zhang (CR10) 2017; 19 Zhang, Liu (CR4) 2005; 42 Ren (CR9) 2016; 46 Chen, Zhang (CR3) 2017; 15 Cochrane (CR7) 2002; 101 Zhang, Li (CR12) 2008 Han (CR5) 2014; 64 Zhang, Han (CR6) 2014; 136 T. Cochrane (1658_CR7) 2002; 101 S.M. Shen (1658_CR1) 2017; 2017 W.P. Zhang (1658_CR12) 2008 G.L. Ren (1658_CR9) 2016; 46 W.P. Zhang (1658_CR6) 2014; 136 W.P. Zhang (1658_CR4) 2005; 42 D. Han (1658_CR5) 2014; 64 Z.Y. Chen (1658_CR3) 2017; 15 X.X. Li (1658_CR2) 2017; 15 T. Cochrane (1658_CR8) 2006; 116 T.M. Apostol (1658_CR13) 1976 W.P. Zhang (1658_CR11) 2018; 20 H. Zhang (1658_CR10) 2017; 19 |
| References_xml | – volume: 116 start-page: 270 year: 2006 end-page: 292 ident: CR8 article-title: Using Stepanov’s method for exponential sums involving rational functions publication-title: J. Number Theory doi: 10.1016/j.jnt.2005.04.001 – volume: 19 start-page: 75 year: 2017 end-page: 83 ident: CR10 article-title: The fourth power mean of two-term exponential sums and its application publication-title: Math. Rep. – volume: 15 start-page: 151 year: 2017 end-page: 156 ident: CR2 article-title: The hybrid power mean quartic Gauss sums and Kloosterman sums publication-title: Open Math. – volume: 46 start-page: 321 issue: 3 year: 2016 end-page: 324 ident: CR9 article-title: On the fourth power mean of one kind special quadratic Gauss sums publication-title: J. Northwest Univ. Nat. Sci. – year: 1976 ident: CR13 publication-title: Introduction to Analytic Number Theory – volume: 101 start-page: 131 year: 2002 end-page: 149 ident: CR7 article-title: Exponential sums modulo prime powers publication-title: Acta Arith. doi: 10.4064/aa101-2-5 – volume: 136 start-page: 403 year: 2014 end-page: 413 ident: CR6 article-title: On the sixth power mean of the two-term exponential sums publication-title: J. Number Theory doi: 10.1016/j.jnt.2013.10.022 – volume: 15 start-page: 1251 year: 2017 end-page: 1255 ident: CR3 article-title: On the fourth-order linear recurrence formula related to classical Gauss sums publication-title: Open Math. – volume: 20 start-page: 73 year: 2018 end-page: 80 ident: CR11 article-title: The number of solutions of the diagonal cubic congruence equation mod publication-title: Math. Rep. – volume: 42 start-page: 189 year: 2005 end-page: 199 ident: CR4 article-title: On the general Gauss sums and their fourth power mean publication-title: Osaka J. Math. – volume: 64 start-page: 53 year: 2014 end-page: 62 ident: CR5 article-title: A hybrid mean value involving two-term exponential sums and polynomial character sums publication-title: Czechoslov. Math. J. doi: 10.1007/s10587-014-0082-0 – volume: 2017 year: 2017 ident: CR1 article-title: On the quartic Gauss sums and their recurrence property publication-title: Adv. Differ. Equ. doi: 10.1186/s13662-017-1097-2 – year: 2008 ident: CR12 publication-title: Elementary Number Theory – volume: 46 start-page: 321 issue: 3 year: 2016 ident: 1658_CR9 publication-title: J. Northwest Univ. Nat. Sci. – volume: 116 start-page: 270 year: 2006 ident: 1658_CR8 publication-title: J. Number Theory doi: 10.1016/j.jnt.2005.04.001 – volume: 20 start-page: 73 year: 2018 ident: 1658_CR11 publication-title: Math. Rep. – volume: 2017 year: 2017 ident: 1658_CR1 publication-title: Adv. Differ. Equ. doi: 10.1186/s13662-017-1097-2 – volume: 101 start-page: 131 year: 2002 ident: 1658_CR7 publication-title: Acta Arith. doi: 10.4064/aa101-2-5 – volume: 19 start-page: 75 year: 2017 ident: 1658_CR10 publication-title: Math. Rep. – volume-title: Introduction to Analytic Number Theory year: 1976 ident: 1658_CR13 – volume: 42 start-page: 189 year: 2005 ident: 1658_CR4 publication-title: Osaka J. Math. – volume: 15 start-page: 1251 year: 2017 ident: 1658_CR3 publication-title: Open Math. doi: 10.1515/math-2017-0104 – volume: 64 start-page: 53 year: 2014 ident: 1658_CR5 publication-title: Czechoslov. Math. J. doi: 10.1007/s10587-014-0082-0 – volume: 136 start-page: 403 year: 2014 ident: 1658_CR6 publication-title: J. Number Theory doi: 10.1016/j.jnt.2013.10.022 – volume: 15 start-page: 151 year: 2017 ident: 1658_CR2 publication-title: Open Math. doi: 10.1515/math-2017-0014 – volume-title: Elementary Number Theory year: 2008 ident: 1658_CR12 |
| SSID | ssj0029488 |
| Score | 2.141744 |
| Snippet | In this paper, we use the analytic method and the properties of classical Gauss sums to study the computational problems of one kind hybrid power mean of... Abstract In this paper, we use the analytic method and the properties of classical Gauss sums to study the computational problems of one kind hybrid power mean... |
| SourceID | doaj proquest crossref springer |
| SourceType | Open Website Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 1 |
| SubjectTerms | Analysis Analytic method Difference and Functional Equations Functional Analysis Hybrid power mean Mathematics Mathematics and Statistics Ordinary Differential Equations Partial Differential Equations Quartic Gauss sums Sums Two-term exponential sums |
| SummonAdditionalLinks | – databaseName: ProQuest Central dbid: BENPR link: http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV1LT9wwEB7R5dIeKvpSQ6HyoadWVpON48QnBIiHkEC0KhI3y6-0B0h2N7tq4dczk3UWqATX2InjeX7jxwzAF6kIRddjbtD5chG85NYKz0NQ3ppQ5csb3qdn8vhCnFwWl3HBrYvHKgeb2Btq3zpaI8cgXVYkLlm5M5lyqhpFu6uxhMYLWEcTXFUjWN87ODv_uQq5lOgrT2YSVYmwQNzXzCr5vctyKelYAkZR6Ib57SPP1Cfwf4Q6_9so7f3P4Qa8jsCR7S45_QbWQvMWXj1IJ_gOfiDP2Z8buoPFJlT9jF0H07C2Zojy2HTRSwk7MouuYzijjpnG903zvy0nE83Cv0nb0PkhHIl6vIeLw4Nf-8c8lkzgDpVvzo1wKhiFTlwWyhn0PL50CGpKfGiLwgfKMJjboi6Vq8allwhXTI1RirRWem_yDzBqcKCPwEKWWuHQoTtfisIK7Ig0tmkIhUeYViaQDuTSLuYTp7IWV7qPKyqplxTWSGFNFNa3CXxdvTJZJtN4rvMe8WDVkfJg9w_a2W8d1UqneVA2F6LGOYrKI3aRJUZA47xWzklvEtgaOKijcnb6XpQS-DZw9b75yT_afP5jn-DlmKSJsm5mWzCazxZhGxHL3H6OYnkHElrmrA priority: 102 providerName: ProQuest – databaseName: Springer Nature OA Free Journals dbid: C6C link: http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LSwMxEA5aL3oQn1itkoMnJbiPbHZz1OIDoYJgwVvIa_Gg2-q2qP31zuxuaxUVPG4yIZuZSeYbknwh5FBIRNF5xDQEX8a9E8wY7pj30hnts7i-4d27EVd9fn2f3Ddk0XgXZn7_PszESRnGQuDhAch1IFiyySJZSsI4xVcauqI7y60kOGKzafljsy9hp2Ln_wIpv-2CVsHlYo2sNqiQntZmXCcLvtggK3NcgfDVmxGslpvkFsxLH97xuhUd4kNn9Mnrgg5yCkL0eVw5BL3U47Kk4Gsl1YWrqkavA4arMfVvw0GBR4WgX5TYIv2L87vuFWteR2AW5tmIaW6l1xLitUik1RBkXGoBv6RQaJLEeSQTjE2Sp9JmUeoEIBOdQ0IijBHO6XibtAroaIdQHwaGW4jd1qU8MRwEIaKZwPvEASJL2ySYKk_ZhjocX7B4VFUKkQlV61uBvhXqW03a5GjWZFjzZvwlfIYWmQki5XVVAJ6gmhmkgthLE3Oewxh55gCmiBSSnSjOpbXC6TbpTO2pmnlYqigQGS4yOIbjqY0_q3_9o91_Se-R5QhdDfk2ww5pjV7Gfh-wysgcVF76AWXc4Pg priority: 102 providerName: Springer Nature |
| Title | The hybrid power mean of the quartic Gauss sums and the two-term exponential sums |
| URI | https://link.springer.com/article/10.1186/s13662-018-1658-z https://www.proquest.com/docview/2068319617 https://doaj.org/article/03e9b344f56048d2936775823f9cc6da |
| Volume | 2018 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV3NS8MwFA9-XPQgfuJ0Sg6elGDXpmlznMMpgkPFgbeQr-JBu2k31P31vtd2OgX14iXQ5JUkLy_5_R5JXgg5EBJZdBYyDeDLuHeCGcMd8146o30aVTe8L3vivM8v7uK7mae-8ExYFR64UtxxEHlpIs4zgGaeOkAnkQDHDaNMWitcSY0A86bOVO1qSbDLeg-zlYrjohUJgUcQwGMCyGWTLyhUBuv_wjC_bYqWWNNdJSs1SaTtqnFrZM7n62R5JnTgBrmG8aX3b3jfig7xpTP66HVOBxkFRkefxmXH6JkeFwUFYyuozl1ZNHoZMFyOqX8dDnI8KwQ1ocQm6XdPbzvnrH4egVmYaCOmuZVeSwBsEUurAWVcYkFLCWSaOHYeowlGJs4SadMwcQKoic7AIxHGCOd0tEUWcqhom1DfCgy3AN7WJTw2HAQB0kzgfeyAkiUNEkzVpWwdOxyfsHhQpQ-RClVpWIGGFWpYTRrk8OOXYRU44zfhExyDD0GMeV1mgCWo2hLUX5bQIM3pCKp6IhYqDESKqwz24Wg6qp_FP7Zo5z9atEuWQrQ5jMPZapKF0fPY7wGHGZl9Ms-DM0jTLqSLJ6e9qxv46ojOfmnIkPbD9jsGIPAJ |
| linkProvider | Directory of Open Access Journals |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Lb9QwEB6VcgAOiKe6UMAHuIAsNonjxAeEymO7pQ8JqZV6M34FDpBsm12V9kfxGzvjJFuKRG-9Ok6cjD_7-ya2ZwBeSkUqukq5QfLlInjJrRWeh6C8NaHMuhPeu3tyeiC-HOaHK_BnOAtD2yqHOTFO1L5x9I8cnXRZElyS4v3siFPWKFpdHVJodLDYDqcn6LK177Y-Yf--StPJ5_2PU95nFeAO8TnnRjgVjEKek7lyBidnXzjk_QILbZ77QEH4MptXhXJlWniJjG4qFPLSWum9yfC5N-CmyJDJ6WT6ZHPp4CkR81wmEgcuKY9-FTUp5ds2yaSkTRDosyHp87NLPBjTBVzSuP8sy0a2m9yDu71MZRsdru7DSqgfwJ2_ghc-hK-IMPbjlE58sRnlWmO_gqlZUzHUlOxoETHJNs2ibRnar2Wm9vHS_KThRAgs_J41Ne1WwpaoxiM4uBZTPobVGhtaAxaSsRUO5YPzhcitwIpIqnYcQu5RFBYjGA_m0q6PXk5JNH7q6MWUUncW1mhhTRbWZyN4vbxl1oXuuKryB-qDZUWKuh0LmuPvuh_EepwFZTMhKvxGUXpUSrJAfyvNKuWc9GYE60MP6n4qaPUFcEfwZujVi8v_faMnVz_sBdya7u_u6J2tve2ncDslZFG8z2QdVufHi_AMtdLcPo8AZfDtukfEOSoqIis |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Lb9QwEB6VrYTggHiKbQv4ABeQ1U3iOPEBVZR2aSmsCqJSb65fgQMk22ZXffw0fh0zeWwpEr31ajt2Mv7s-SYezwC8lIpYdBFzg8qXi-Alt1Z4HoLy1oQ8aW94f57InQPx8TA9XILf_V0Ycqvs98Rmo_aVo3_kaKTLnOASZetF5xaxvzXemB5zyiBFJ619Oo0WInvh_BTNt_rt7hbO9as4Hm9_e7_DuwwD3CFWZ9wIp4JRqPNkqpzBjdpnDjlAhoU2TX2ggHyJTYtMuTzOvETtbgok9dJa6b1JsN9bsJyRVTSA5c3tyf7XhbmnRJP1MpK4jImHdGeqUS7X6yiRklwi0IJDCsAvrmjFJnnAFcb7zyFto_vG9-FeR1rZuxZlD2AplA_h7l-hDB_BF8Qb-3FO97_YlDKvsV_BlKwqGDJMdjxvEMo-mHldM5RgzUzpm6rZacVJPbBwNq1K8l3CkajFYzi4EWE-gUGJAz0FFqKRFQ7JhPOZSK3Ahqhi7SiE1CNFzIYw6sWlXRfLnFJq_NSNTZNL3UpYo4Q1SVhfDOH14pFpG8jjusabNAeLhhSDuymoTr7rbknrURKUTYQo8BtF7pE3yQytrzgplHPSmyGs9TOou42h1pcwHsKbflYvq__7RivXd_YCbuNq0J92J3urcCcmYFHwz2gNBrOTeXiGxGlmn3cIZXB004viD7J6J70 |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=The+hybrid+power+mean+of+the+quartic+Gauss+sums+and+the+two-term+exponential+sums&rft.jtitle=Advances+in+difference+equations&rft.au=Xiaoxue+Li&rft.date=2018-07-11&rft.pub=SpringerOpen&rft.eissn=1687-1847&rft.volume=2018&rft.issue=1&rft.spage=1&rft.epage=10&rft_id=info:doi/10.1186%2Fs13662-018-1658-z&rft.externalDBID=DOA&rft.externalDocID=oai_doaj_org_article_03e9b344f56048d2936775823f9cc6da |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1687-1847&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1687-1847&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1687-1847&client=summon |